The feedback budget

Two questions, in the order the physics asks them. First: is the retained feedback momentum enough to lift the residual gas out of the cloud's potential? Then, if it is: do the stars stay bound once the gas — most of the mass — is gone? Five of these six environments clear their gas. The most massive and most tightly bound cloud does not: the cost of lifting the gas grows with cloud mass faster than the cluster's output grows with its stars, and that cloud's escape speed also exceeds the sound speed of photoionized gas, so its H II region is trapped and one channel switches off entirely. Every cluster stays bound either way — and that is not a verdict the budget decides. These clusters are born far below virial equilibrium, so the stars' own self-gravity holds them whatever the gas does.

The three channels deposit momentum on different schedules. Winds and radiation inject at a constant rate while the stars sit on the main sequence, so they accumulate linearly; the H II curve is the Spitzer solution for an ionization front recomputed at each step, and although the front decelerates, the shell it sweeps grows faster still, so photoionization accumulates faster than linearly until it runs out of cloud. Winds enter differently again: Weaver's similarity solution sets the ceiling on what a hot bubble could deliver, and how much survives cooling is calibrated so the momentum boost matches what three-dimensional simulations of wind-blown bubbles measure, rather than chosen to look reasonable.

The controls above expose the two quantities this accounting is least sure of.Shell covering is one slider rather than two because it is one physical structure: the same holes that let starlight escape without ever touching the gas also let the hot shocked wind vent out of them. How strongly those are tied together is itself unsettled — the two published treatments offered here disagree about the wind boost by roughly a factor of five, and switching between them is the honest way to see that rather than hide it inside a default.H II leakage has no measurement behind it at all; it is a placed number, which is exactly why it should be something you can move. Both wind recipes are calibrated independently, so switching recipe switches its leakage with it.

The gas balloons outward as the budget clears it, revealing the bare cluster — a legible stand-in for the anisotropic champagne flows and blister breakouts a full radiation-hydrodynamics run resolves. That physics is what my research code models; this piece makes its accounting visible.